Production of light-flavor hadrons in pp collisions at $\sqrt{s}~=~7\text { and }\sqrt{s} = 13 \, \text { TeV} $

The ALICE collaboration Acharya, Shreyasi ; Adamova, Dagmar ; Adler, Alexander ; et al.
Eur.Phys.J.C 81 (2021) 256, 2021.
Inspire Record 1797443 DOI 10.17182/hepdata.100303

The production of $\pi^{\pm}$, $\rm{K}^{\pm}$, $\rm{K}^{0}_{S}$, $\rm{K}*(892)^{0}$, $\rm{p}$, $\phi(1020)$, $\Lambda$, $\Xi^{-}$, $\Omega^{-}$, and their antiparticles was measured in inelastic proton-proton (pp) collisions at a center-of-mass energy of $\sqrt{s}$ = 13 TeV at midrapidity ($|y|<0.5$) as a function of transverse momentum ($p_{\rm{T}}$) using the ALICE detector at the CERN LHC. Furthermore, the single-particle $p_{\rm{T}}$ distributions of $\rm{K}^{0}_{S}$, $\Lambda$, and $\overline{\Lambda}$ in inelastic pp collisions at $\sqrt{s}$ = 7 TeV are reported here for the first time. The $p_{\rm{T}}$ distributions are studied at midrapidity within the transverse momentum range $0\leq p_{\rm{T}}\leq20$ GeV/$c$, depending on the particle species. The $p_{\rm{T}}$ spectra, integrated yields, and particle yield ratios are discussed as a function of collision energy and compared with measurements at lower $\sqrt{s}$ and with results from various general-purpose QCD-inspired Monte Carlo models. A hardening of the spectra at high $p_{\rm{T}}$ with increasing collision energy is observed, which is similar for all particle species under study. The transverse mass and $x_{\rm{T}}\equiv2p_{\rm{T}}/\sqrt{s}$ scaling properties of hadron production are also studied. As the collision energy increases from $\sqrt{s}$ = 7 to 13 TeV, the yields of non- and single-strange hadrons normalized to the pion yields remain approximately constant as a function of $\sqrt{s}$, while ratios for multi-strange hadrons indicate enhancements. The $p_{\rm{T}}$-differential cross sections of $\pi^{\pm}$, $\rm{K}^{\pm}$ and $\rm{p}$ ($\overline{\rm{p}}$) are compared with next-to-leading order perturbative QCD calculations, which are found to overestimate the cross sections for $\pi^{\pm}$ and $\rm{p}$ ($\overline{\rm{p}}$) at high $p_{\rm{T}}$.

47 data tables

Transverse momentum spectrum of $\pi^{+} + \pi^{-}$ measured at midrapidity ($|y|<0.5$) in inelastic pp collisions at $\sqrt{s}$ = 13 TeV. The normalization uncertainty of $\pm2.6\%$ is excluded.

Transverse momentum spectrum of $K^{+} + K^{-}$ measured at midrapidity ($|y|<0.5$) in inelastic pp collisions at $\sqrt{s}$ = 13 TeV. The normalization uncertainty of $\pm2.6\%$ is excluded.

Transverse momentum spectrum of $K^{0}_{S}$ measured at midrapidity ($|y|<0.5$) in inelastic pp collisions at $\sqrt{s}$ = 13 TeV. The normalization uncertainty of $\pm2.6\%$ is excluded.

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J/$\psi$ production as a function of charged-particle multiplicity in p-Pb collisions at $\sqrt{\textit{s}_{\rm NN}}~=~8.16$ TeV

The ALICE collaboration Acharya, Shreyasi ; Adamova, Dagmar ; Adler, Alexander ; et al.
JHEP 09 (2020) 162, 2020.
Inspire Record 1792996 DOI 10.17182/hepdata.97018

Inclusive J/$\psi$ yields and average transverse momenta in p-Pb collisions at a center-of-mass energy per nucleon pair $\sqrt{s_{\rm NN}}$ = 8.16 TeV are measured as a function of the charged-particle pseudorapidity density with ALICE. The J/$\psi$ mesons are reconstructed at forward $(2.03 < y_{\rm cms} < 3.53)$ and backward ($-4.46 < y_{\rm cms} < -2.96$) center-of-mass rapidity in their dimuon decay channel while the charged-particle pseudorapidity density is measured around midrapidity. The J/$\psi$ yields at forward and backward rapidity normalized to their respective average values increase with the normalized charged-particle pseudorapidity density, the former showing a weaker increase than the latter. The normalized average transverse momenta at forward and backward rapidity manifest a steady increase from low to high charged-particle pseudorapidity density with a saturation beyond the average value.

6 data tables

Relative yield of inclusive J/psi as a function of relative charged-particle pseudorapidity density at forward rapidity 2.03 < y_cms < 3.53 (p-going direction).

Relative yield of inclusive J/psi as a function of relative charged-particle pseudorapidity density at backward rapidity -4.46 < y_cms < -2.96 (Pb-going direction).

Mean transverse momentum of inclusive J/psi as a function of the relative charged-particle pseudorapidity density at forward rapidity 2.03 < y_cms < 3.53 (p-going direction).

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Production of (anti-)$^3$He and (anti-)$^3$H in p-Pb collisions at $\sqrt{s_{\rm{NN}}}$ = 5.02 TeV

The ALICE collaboration Acharya, Shreyasi ; Adamova, Dagmar ; Adler, Alexander ; et al.
Phys.Rev.C 101 (2020) 044906, 2020.
Inspire Record 1762356 DOI 10.17182/hepdata.94416

The transverse momentum ($p_{\rm{T}}$) differential yields of (anti-)$^3$He and (anti-)$^3$H measured in p-Pb collisions at $\sqrt{s_{\rm{NN}}}$ = 5.02 TeV with ALICE at the Large Hadron Collider (LHC) are presented. The ratios of the $p_{\rm{T}}$-integrated yields of (anti-)$^3$He and (anti-)$^3$H to the proton yields are reported, as well as the $p_{\rm{T}}$ dependence of the coalescence parameters $B_3$ for (anti-)$^3$He and (anti-)$^3$H. For (anti-)$^3$He, the results obtained in four classes of the mean charged-particle multiplicity density are also discussed. These results are compared to predictions from a canonical statistical hadronization model and coalescence approaches. An upper limit on the total yield of $^4\bar{\mathrm{He}}$ is determined.

24 data tables

Transverse momentum spectra of (anti-)$^3\mathrm{He}$ measured in $\mathrm{INEL}>0$ p--Pb collisions at $\sqrt{s_\mathrm{NN}} = 5.02$

Transverse momentum spectra of (anti-)$^3\mathrm{H}$ measured in $\mathrm{INEL}>0$ p--Pb collisions at $\sqrt{s_\mathrm{NN}} = 5.02$

$^3\overline{\mathrm{He}} /\,^3\mathrm{He}$ ratio in $\mathrm{INEL}>0$ p--Pb collisions at $\sqrt{s_\mathrm{NN}} = 5.02$

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Version 2
$\pi ^{0}$ and $\eta $ meson production in proton-proton collisions at $\sqrt{s}=8$ TeV

The ALICE collaboration Acharya, Shreyasi ; Adam, Jaroslav ; Adamova, Dagmar ; et al.
Eur.Phys.J.C 78 (2018) 263, 2018.
Inspire Record 1620477 DOI 10.17182/hepdata.79044

An invariant differential cross section measurement of inclusive $\pi^{0}$ and $\eta$ meson production at mid-rapidity in pp collisions at $\sqrt{s}=8$ TeV was carried out by the ALICE experiment at the LHC. The spectra of $\pi^{0}$ and $\eta$ mesons were measured in transverse momentum ranges of $0.3<p_{\rm T}<35$ GeV/$c$ and $0.5<p_{\rm T}<35$ GeV/$c$, respectively. Next-to-leading order perturbative QCD calculations using fragmentation functions DSS14 for the $\pi^{0}$ and AESSS for the $\eta$ overestimate the cross sections of both neutral mesons, although such calculations agree with the measured $\eta/\pi^{0}$ ratio within uncertainties. The results were also compared with PYTHIA~8.2 predictions for which the Monash~2013 tune yields the best agreement with the measured neutral meson spectra. The measurements confirm a universal behavior of the $\eta/\pi^{0}$ ratio seen for NA27, PHENIX and ALICE data for pp collisions from $\sqrt{s}=27.5$ GeV to $\sqrt{s}=8$ TeV within experimental uncertainties. A relation between the $\pi^{0}$ and $\eta$ production cross sections for pp collisions at $\sqrt{s}=8$ TeV is given by $m_{\rm T}$ scaling for $p_{\rm T}>3.5$ GeV/$c$. However, a deviation from this empirical scaling rule is observed for transverse momenta below $p_{\rm T}<3.5$ GeV/$c$ in the $\eta/\pi^0$ ratio with a significance of $6.2\sigma$.

8 data tables

Invariant differential cross section of $\pi^0$ produced in inelastic pp collisions at center-of-mass energy 8 TeV, the uncertainty of $\sigma_{MB}$ of 2.6% is not included in the systematic error.

Invariant differential cross section of $\eta$ produced in inelastic pp collisions at center-of-mass energy 8 TeV, the uncertainty of $\sigma_{MB}$ of 2.6% is not included in the systematic error.

Integrated yields of $\pi^0$ mesons produced in inelastic pp collisions at center-of-mass energies of 2.76 and 8 TeV. The uncertainties of $\sigma_{MB}$ of $^{+3.9\%}_{-6.4\%}(model)\pm2.0(lumi)$% for $\sqrt{s}=2.76$ TeV and $\pm2.3$% for 8 TeV are not included in the systematic error.

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Energy dependence of forward-rapidity $\mathrm {J}/\psi $ and $\psi \mathrm {(2S)}$ production in pp collisions at the LHC

The ALICE collaboration Acharya, Shreyasi ; Adamova, Dagmar ; Aggarwal, Madan Mohan ; et al.
Eur.Phys.J.C 77 (2017) 392, 2017.
Inspire Record 1511865 DOI 10.17182/hepdata.77781

We present results on transverse momentum ($p_{\rm T}$) and rapidity ($y$) differential production cross sections, mean transverse momentum and mean transverse momentum square of inclusive J/$\psi$ and $\psi(2S)$ at forward rapidity ($2.5<y<4$) as well as $\psi(2S)$-to-J/$\psi$ cross section ratios. These quantities are measured in pp collisions at center of mass energies $\sqrt{s}=5.02$ and 13 TeV with the ALICE detector. Both charmonium states are reconstructed in the dimuon decay channel, using the muon spectrometer. A comprehensive comparison to inclusive charmonium cross sections measured at $\sqrt{s}=2.76$, 7 and 8 TeV is performed. A comparison to non-relativistic quantum chromodynamics and fixed-order next-to-leading logarithm calculations, which describe prompt and non-prompt charmonium production respectively, is also presented. A good description of the data is obtained over the full $p_{\rm T}$ range, provided that both contributions are summed. In particular, it is found that for $p_{\rm T}>15$ GeV/$c$ the non-prompt contribution reaches up to 50% of the total charmonium yield.

14 data tables

Differential production cross sections of $J/\psi$ as a function of $p_{\rm T}$.

Differential production cross sections of $J/\psi$ as a function of rapidity.

Differential production cross sections of $\psi(2S)$ as a function of $p_{\rm T}$.

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$D$-meson production in $p$-Pb collisions at $\sqrt{s_{\rm NN}}=$5.02 TeV and in pp collisions at $\sqrt{s}=$7 TeV

The ALICE collaboration Adam, Jaroslav ; Adamova, Dagmar ; Aggarwal, Madan Mohan ; et al.
Phys.Rev.C 94 (2016) 054908, 2016.
Inspire Record 1465513 DOI 10.17182/hepdata.73941

The production cross sections of the prompt charmed mesons D$^0$, D$^+$, D$^{*+}$ and D$_s$ were measured at mid-rapidity in p-Pb collisions at a centre-of-mass energy per nucleon pair $\sqrt{s_{\rm NN}}=5.02$ TeV with the ALICE detector at the LHC. D mesons were reconstructed from their decays D$^0\rightarrow{\rm K}^-\pi^+$, D$^+\rightarrow{\rm K}^-\pi^+\pi^+$, D$^{*+}\rightarrow D^0\pi^+$, D$_s^+\rightarrow\phi\pi^+\rightarrow{\rm K}^-{\rm K}^+\pi^+$, and their charge conjugates. The $p_{\rm T}$-differential production cross sections were measured at mid-rapidity in the interval $1<p_{\rm T}<24$ GeV/$c$ for D$^0$, D$^+$ and D$^{*+}$ mesons and in $2<p_{\rm T}<12$ GeV/$c$ for D$_s$ mesons, using an analysis method based on the selection of decay topologies displaced from the interaction vertex. The production cross sections of the D$^0$, D$^+$ and D$^{*+}$ mesons were also measured in three $p_{\rm T}$ intervals as a function of the rapidity $y_{\rm cms}$ in the centre-of-mass system in $-1.26<y_{\rm cms}<0.34$. In addition, the prompt D$^0$ cross section was measured in pp collisions at $\sqrt{s}=7$ TeV and p-Pb collisions at $\sqrt{s_{\rm NN}}=5.02$ TeV down to $p_{\rm T}=0$ using an analysis technique that is based on the estimation and subtraction of the combinatorial background, without reconstruction of the D$^0$ decay vertex. The nuclear modification factor $R_{\rm pPb}(p_{\rm T})$, defined as the ratio of the $p_{\rm T}$-differential D-meson cross section in p-Pb collisions and that in pp collisions scaled by the mass number of the Pb nucleus, was calculated for the four D-meson species and found to be compatible with unity within experimental uncertainties. The results are compared to theoretical calculations that include cold-nuclear-matter effects and to transport model calculations incorporating the interactions of charm quarks with an expanding deconfined medium.

21 data tables

pT-differential cross section of inclusive Dzero mesons in pp collisions at sqrt{sNN}=7 TeV in the rapidity interval |y|<0.5. Branching ratio of D0->Kpi : 0.0388.

pT-differential cross section of prompt Dzero mesons in pp collisions at sqrt{sNN}=7 TeV in the rapidity interval |y|<0.5. Branching ratio of D0->Kpi : 0.0388. Data points for pt<2 GeV/c from analysis "without vertexing". Data points for pt>2 GeV/c from the analysis "with vertexing" taken from JHEP 1201 (2012) 128 (http://hepdata.cedar.ac.uk/view/ins944757) and corrected for the updated BR value.

First column: production cross sections per unit of rapidity for prompt D0 mesons, inclusive D0 mesons (no feed-down subtraction) and charm quarks at mid-rapidity in pp collisions at 7 TeV. For D0 mesons, the second (sys) error is from the luminosity uncertainty, the third (sys) error is from the branching-ratio uncertainties. For charm quarks, the second (sys) error is from the luminosity uncertainty, the third (sys) error is from the Fragmentation Function uncertainties, the fourth (sys) error is from the rapidity shapes of D0 mesons and single charm quarks. Second column: total production cross sections, extrapolated to the full phase space, for prompt D0 mesons and charm quarks. For D0 mesons, the second (sys) error is the from the extrapolation uncertainty, the third from the luminosity uncertainty and the fourth from the branching-ratio uncertainties. For charm quarks, the second (sys) error is from the extrapolation, the third is from the luminosity uncertainty and the fourth is from the Fragmentation Function uncertainties. Third column: value of <pT> of prompt D0 mesons. The first uncertainty is statistical, the second is the systematic uncertainty.

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Production of K$^{*}$ (892)$^{0}$ and $\phi $ (1020) in p–Pb collisions at $\sqrt{s_{{\text {NN}}}}$ = 5.02 TeV

The ALICE collaboration Adam, Jaroslav ; Adamova, Dagmar ; Aggarwal, Madan Mohan ; et al.
Eur.Phys.J.C 76 (2016) 245, 2016.
Inspire Record 1418181 DOI 10.17182/hepdata.72720

The production of K$^{*}$(892)$^{0}$ and $\phi$(1020) mesons has been measured in p-Pb collisions at $\sqrt{s_{\mathrm{NN}}}$ = 5.02 TeV. K$^{*0}$ and $\phi$ are reconstructed via their decay into charged hadrons with the ALICE detector in the rapidity range $-0.5 < y <0$. The transverse momentum spectra, measured as a function of the multiplicity, have p$_{\mathrm{T}}$ range from 0 to 15 GeV/$c$ for K$^{*0}$ and from 0.3 to 21 GeV/$c$ for $\phi$. Integrated yields, mean transverse momenta and particle ratios are reported and compared with results in pp collisions at $\sqrt{s}$ = 7 TeV and Pb-Pb collisions at $\sqrt{s_{\mathrm{NN}}}$ = 2.76 TeV. In Pb-Pb and p-Pb collisions, K$^{*0}$ and $\phi$ probe the hadronic phase of the system and contribute to the study of particle formation mechanisms by comparison with other identified hadrons. For this purpose, the mean transverse momenta and the differential proton-to-$\phi$ ratio are discussed as a function of the multiplicity of the event. The short-lived K$^{*0}$ is measured to investigate re-scattering effects, believed to be related to the size of the system and to the lifetime of the hadronic phase.

30 data tables

Average charged particle pseudo-rapidity density, $\langle\mathrm{d}N_{\rm ch}/\mathrm{d}\eta_{\mathrm{lab}}\rangle$, measured at mid-rapidity in visible cross section event classes and average number of colliding nucleons, $\langle\mathrm{N_{coll}}\rangle$. Multiplicity classes are defined using the V0A estimator; values for $\langle\mathrm{d}N_{\rm ch}/\mathrm{d}\eta_{\mathrm{lab}}\rangle$ are corrected for vertexing and trigger efficiency. Since statistical uncertainties are negligible, only total systematic uncertainties are reported.

$p_{\rm T}$-differential yield of (K$^{*0}$ + $\overline{K^{*0}}$)/2 in p-Pb collisions with centre-of-mass energy/nucleon=5.02 TeV (NSD). Additional systematic error: +- 3.1% (normalization).

$p_{\rm T}$-differential yield of (K$^{*0}$ + $\overline{K^{*0}}$)/2 in p-Pb collisions with centre-of-mass energy/nucleon=5.02 TeV (0-20% multiplicity class).

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Multi-strange baryon production in p-Pb collisions at $\sqrt{s_\mathbf{NN}}=5.02$ TeV

The ALICE collaboration Adam, Jaroslav ; Adamova, Dagmar ; Aggarwal, Madan Mohan ; et al.
Phys.Lett.B 758 (2016) 389-401, 2016.
Inspire Record 1411084 DOI 10.17182/hepdata.73011

The multi-strange baryon yields in Pb--Pb collisions have been shown to exhibit an enhancement relative to pp reactions. In this work, $\Xi$ and $\Omega$ production rates have been measured with the ALICE experiment as a function of transverse momentum, ${p_{\rm T}}$, in p-Pb collisions at a centre-of-mass energy of ${\sqrt{s_{\rm NN}}}$ = 5.02 TeV. The results cover the kinematic ranges 0.6 GeV/$c<{p_{\rm T}} <$7.2 GeV/$c$ and 0.8 GeV/$c<{p_{\rm T}}<$ 5 GeV/$c$, for $\Xi$ and $\Omega$ respectively, in the common rapidity interval -0.5 $<{y_{\rm CMS}}<$ 0. Multi-strange baryons have been identified by reconstructing their weak decays into charged particles. The ${p_{\rm T}}$ spectra are analysed as a function of event charged-particle multiplicity, which in p-Pb collisions ranges over one order of magnitude and lies between those observed in pp and Pb-Pb collisions. The measured ${p_{\rm T}}$ distributions are compared to the expectations from a Blast-Wave model. The parameters which describe the production of lighter hadron species also describe the hyperon spectra in high multiplicity p-Pb. The yield of hyperons relative to charged pions is studied and compared with results from pp and Pb-Pb collisions. A statistical model is employed, which describes the change in the ratios with volume using a canonical suppression mechanism, in which the small volume causes a species-dependent relative reduction of hadron production. The calculations, in which the magnitude of the effect depends on the strangeness content, show good qualitative agreement with the data.

24 data tables

Xi pt spectrum in 0-5% multiplicity class.

Xi pt spectrum in 5-10% multiplicity class.

Xi pt spectrum in 10-20% multiplicity class.

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Differential studies of inclusive J/ψ and ψ(2S) production at forward rapidity in Pb-Pb collisions at $ \sqrt{s_{\mathrm{NN}}}=2.76 $ TeV

The ALICE collaboration Adam, Jaroslav ; Adamova, Dagmar ; Aggarwal, Madan Mohan ; et al.
JHEP 05 (2016) 179, 2016.
Inspire Record 1380192 DOI 10.17182/hepdata.73094

The production of J/$\psi$ and $\psi(2S)$ was measured with the ALICE detector in Pb-Pb collisions at the LHC. The measurement was performed at forward rapidity ($2.5 < y < 4 $) down to zero transverse momentum ($p_{\rm T}$) in the dimuon decay channel. Inclusive J/$\psi$ yields were extracted in different centrality classes and the centrality dependence of the average $p_{\rm T}$ is presented. The J/$\psi$ suppression, quantified with the nuclear modification factor ($R_{\rm AA}$), was studied as a function of centrality, transverse momentum and rapidity. Comparisons with similar measurements at lower collision energy and theoretical models indicate that the J/$\psi$ production is the result of an interplay between color screening and recombination mechanisms in a deconfined partonic medium, or at its hadronization. Results on the $\psi(2S)$ suppression are provided via the ratio of $\psi(2S)$ over J/$\psi$ measured in pp and Pb-Pb collisions.

16 data tables

Values of $\langle p_{\rm T}\rangle$ and $\langle p^2_{\rm T}\rangle$ of inclusive J/$\psi$ measured in $0<p_{\rm T}<8$ GeV/$c$ and $2.5<y<4$. Statistical and systematic uncertainties are also reported.

Inclusive J/$\psi$ yields in $p_{\rm T}$ intervals for the 0-20%, 20-40% and 40-90% most central Pb-Pb collisions. The rapidity range is $2.5<y<4$. Statistical and systematic uncertainties are also reported. A global systematic uncertainty of 4% affects all the values. A 2%, 1% and 2% systematic uncertainty, independent of $p_{\rm T}$, affects the centrality classes 0-20%, 20-40% and 40-90%, respectively.

Inclusive J/$\psi$ $R_{\rm AA}$ and Pb-Pb yields as a function of centrality, $p_{\rm T}<8$ GeV/$c$ and $2.5<y<4.0$. Statistical and systematic uncertainties are also reported. A global systematic uncertainty of 15% (12%) affects all the $R_{\rm AA}$ (yields) values.

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Inclusive, prompt and non-prompt J/$\psi$ production at mid-rapidity in Pb-Pb collisions at $\sqrt{s_{\rm NN}}$ = 2.76 TeV

The ALICE collaboration Adam, Jaroslav ; Adamova, Dagmar ; Aggarwal, Madan Mohan ; et al.
JHEP 07 (2015) 051, 2015.
Inspire Record 1364887 DOI 10.17182/hepdata.68881

The transverse momentum ($p_{\rm T}$) dependence of the nuclear modification factor $R_{\rm AA}$ and the centrality dependence of the average transverse momentum $\langle p_{\rm T}\rangle$ for inclusive J/$\psi$ have been measured with ALICE for Pb-Pb collisions at $\sqrt{s_{\rm NN}}$ = 2.76 TeV in the e$^+$e$^-$ decay channel at mid-rapidity ($|y|<0.8$). The $\langle p_{\rm T}\rangle$ is significantly smaller than the one observed for pp collisions at the same centre-of-mass energy. Consistently, an increase of $R_{\rm AA}$ is observed towards low $p_{\rm T}$. These observations might be indicative of a sizable contribution of charm quark coalescence to the J/$\psi$ production. Additionally, the fraction of non-prompt J/$\psi$ from beauty hadron decays, $f_{\rm B}$, has been determined in the region $1.5 < p_{\rm T} < 10$ GeV/c in three centrality intervals. No significant centrality dependence of $f_{\rm B}$ is observed. Finally, the $R_{\rm AA}$ of non-prompt J/$\psi$ is discussed and compared with model predictions. The nuclear modification in the region $4.5 < p_{\rm T} < 10$ GeV/c is found to be stronger than predicted by most models.

9 data tables

The average transverse momentum $\langle p_{\rm T} \rangle$ of inclusive J/$\psi$ measured at mid-rapidity in centrality selected Pb-Pb collisions as a function of the number of participants.

The average transverse momentum squared $\langle p_{\rm T}^{2} \rangle$ of inclusive J/$\psi$ measured at mid-rapidity in centrality selected Pb-Pb collisions as a function of the number of participants.

The ratio $\langle p_{\rm T}^{2} \rangle_{\rm AA} / \langle p_{\rm T}^{2} \rangle_{\rm pp}$ of inclusive J/$\psi$ measured at mid-rapidity in centrality selected Pb-Pb collisions as a function of the number of participants.

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